Abstract

This paper is devoted to the mathematical rationale of the Kapitsa's hypothesis about interference nature of the phenomenon known as “ball lightning.” It is shown that (i) there are exact solutions of the free Maxwell equations in vacuum describing closed spherical magnetic surfaces (with a tangential time dependent magnetic field, and without an electric field) and (ii) ring-like formations with tangential time-dependent electric field (and with a zero magnetic field everywhere on the ring). It is concluded that the form of these spheres and rings does not suffer changes with time